Traditional approaches for performing adaptive equalization on a signal received from a channel associated with inter-symbol interference (ISI) typically involve conventional filtering techniques such as analog-to-digital conversion followed by processing by a digital finite impulse response (FIR) filter, use of an analog traveling wave FIR filter, or use of a tapped delay line FIR filter. Digital FIR filters are associated with fundamental limitations that become greatly exacerbated in dealing with wide bandwidth signals found in high-speed channels. At the same time, known analog techniques typically suffer from cumbersome implementation.
FIG. 1 is a system level block diagram of a communication link in which a signal containing data is transmitted and received over a channel associated with noise and ISI, and adaptive equalization is applied to the received signal in attempting to mitigate effects of ISI. As shown, the transmitter generates source data represented by a sequence of independent, identically distributed (i.i.d.) random impulse train
                              s          ⁡                      (            t            )                          =                              ∑            n                    ⁢                                    a              n                        ⁢                                                  ⁢                          δ              ⁡                              (                                  t                  -                  nT                                )                                                                        (        1        )            where αn∈{0,1} and can take on either value with equal probability. While this particular impulse train is illustrated as an example, the invention is not necessarily limited to use in conjunction with i.i.d. signals. Similarly the use of a two-level signal is also presented here for purposes of illustration, and the invention needs not necessarily be limited to two-level signals. 1/T corresponds to the bit rate. Non-return to zero (NRZ) transmission is shown here, so that the random impulse train from the source is filtered by a filter with a rectangular impulse response of height unity & width T. As shown in the figure, a 4th order Bessel filter is presented to model the finite bandwidth of the transmitter. One 3 dB bandwidth for the transmit filter may be 0.7/T Hz. The channel may be a high-speed channel such as an optical fiber channel. The channel may also comprise another type of medium, such as copper wire. The channel may be associated with various forms of inter-symbol interference (ISI), such as Polarization Mode Dispersion (PMD), Chromatic Dispersion (CMD), Differential Mode Delay (DMD), and others. For example, for a channel impaired with PMD, the channel impulse response may be written ash(t)=αδ(t)+(1−α)δ(t−τ)  (2)where 0≦α≦1 is the power split parameter and τ is the differential group delay (DGD). Here, Additive White Gaussian Noise (AWGN) of two sided spectral density No/2 is shown to be introduced. There may be various ways in which noise is introduced. For example, in an optoelectronic transceiver, a photo receiver may add noise. In other communication channels, the receiver front end may be the dominant source of noise. Furthermore, other types of processing as well as the channel itself may also be sources of noise.
As shown in FIG. 1, the receiver includes a noise filter followed by an adaptive equalizer. Here, the noise filter is modeled by a 4th order Butterworth filter, and its impulse response is denoted by haa(t). The receiver is shown to also include an equalizer block, a decision element, and an adaptation block, which may together represent a general structure for implementing adaptive equalization to mitigate effect of ISI.
While FIG. 1 illustrates a general structure for performing adaptive equalization, implementation of a particular adaptive equalization technique may be especially challenging. Traditional approaches for performing filtering operations for adaptive equalization are associated with substantial shortcomings, especially when implemented at high data rates. These traditional approaches include use of digital FIR filters as well as traveling wave FIR filters.
A fundamental problem associated with digital FIR filters relates to the wide bandwidth of signals from high-speed channels, which requires substantial amounts of signal processing to be performed at extremely high speeds. In this approach, the received signal is typically digitized by a high speed analog-to-digital converter (ADC) after noise filtering, and filtering is accomplished digitally such as by use of a digital signal processor (DSP). To obtain equalizer performance that is insensitive to the sampling phase of the ADC, the sampling frequency may be specified at double the baud rate, so that a fractionally spaced equalizer can be implemented. While this is straightforward at low data rates, it is an extremely difficult to accomplish at high speeds, in terms of both power dissipation and area efficiency. Thus, use of a DSP FIR filter for performing adaptive equalization on signals derived from high speed channels may be prohibitively costly and impracticable.
A traveling wave FIR filter represents a continuous-time approach to adaptive equalization but presents significant limitations of its own. FIG. 2 illustrates a circuit diagram for a 3-tap example of a traveling wave FIR filter along with a corresponding impulse response plot. The traveling wave FIR filter is comparable to a traveling wave amplifier, but with the output being taken at the “anti-sync” end, as shown in FIG. 2. The filter has two sections of cascaded transmission lines, one on the input side and one on the output side. The illustrated impulse response of the filter may be written ash(t)=w1hw1(t)+w2hw2(t)+w3hw3(t)  (3)hw1 (t) is the impulse response of the filter with w1=1 and w2, w3=0. hw2(t) and hw3(t) are similarly defined. These responses are shown in FIG. 2. In this example, it is assumed that the termination resistors are equal to the characteristic impedance of the transmission lines used for the input and output lines of the filter. Ideally,hw1(t)=w1δ(t)  (4)hw2(t)=w2δ(t−2T)  (5)hw3(t)=w3δ(t−2T)  (6)
High bandwidth transmission lines may be required for operation of a traveling wave FIR filter. This means that low loss transmission lines with bandwidths in excess of the data rates may be necessary. Because transmission lines are cascaded in order to achieve the desired delay, problems associated with finite bandwidth and loss are exacerbated when a large number of taps are required. Low loss transmission lines can be obtained through well known techniques such as patterned ground shield inductors. However, to reach bandwidths of the line that exceed the data rate, inductors may be required to be wound loosely, resulting in excessive area occupied by the filter. This problem is further aggravated by the requirement of providing transmission lines in both the input and output lines. Further, the adaptation of the filter coefficients for a traveling wave FIR filter also presents substantial difficulties. Hardware efficient coefficient adaptation using a least mean square (LMS) algorithm or other algorithms may require access to gradient signals that represent the derivative of the output signal with respect to the tap weights. In a traveling wave FIR filter, however, gradient signals are typically not available. Thus, use of traveling wave FIR filter may preclude the direct use of an LMS algorithm to adaptively determine the filter tap weights.
FIG. 3 illustrates equalization performed using a traditional FIR filter, such as a traveling wave FIR filter or a tapped delay line FIR filter as described above. As shown in the figure, a signal from the communication channel is equalized by a tapped delay line 4-tap (T/2) spaced FIR filter, followed by a sampler and decision device. The filter is driven by the channel output. If a single symbol is assumed to excite the channel input, the FIR filter input is a waveform which is the convolution of the transmit pulse shape (NRZ in this example) with the channel impulse response. Successive taps of the equalizer produce outputs which are convolved versions of the channel output and tap impulse responses. For the fractionally spaced equalizer being considered here, the tap outputs are delayed versions of the channel output, as shown in the figure. These taps outputs are combined with weighting factors w1, w2, w3, and w4, which may be determined prior to the filtering process to minimize ISI at the output of the equalizer.
Here, the equalizer output is decomposed as the weighted sum of four filtered versions of the input signal. These four filtered signals are time limited to 5T in this example. The impulse responses corresponding to the taps are four time limited orthogonal pulses {φF1, φF2, φF3, φF4}. As shown, these are Dirac delta functions with infinite bandwidth, at least in theory. The decision process may be based on the output of a sampler (not shown) sampling the final signal in FIG. 3. It can be seen that the tap impulse responses contain very high frequency components. An implementation of the equalizer illustrated in FIG. 3 would thus require the use of wideband delay elements, which may be associated with greater power and area consumption. For example, this may place geometric constraints on the transmission lines previously described with respect to traveling wave filters.
Accordingly, there exists a significant need for performing filtering operations for adaptive equalization in a power and area efficient manner, especially for equalization of signals associated with high speed channels.